After twenty years of doing this I completely agree with everything, including the doubling of rates. Those cheap clients you reference are inevitably the nightmare clients who will waste your time, put no value on your work, and never send you referral business.
If a new freelancer can’t handle saying no, there is another approach: Always quote by project, not by hours and don’t talk about hourly rates. Then get faster. If I estimate a project at 20 hours, I’m basing it on what someone with less experience might take to complete it. But I know I can get it done in less than half that. Assuming a client is getting quote from others (which they rarely are these days), I look at what I think the competition will be quoting. If they are an agency, I know I’m going to kill them quote-wise (because of mark-up and bloated overhead) . So, if I quote someone $2000 for a twenty hour project and get it done in 8 hours, I’m quoting at $100/hour but making $250/hour. If you’re a beginner these numbers may seem ridiculous but I have two projects going right now in that exact scenario. The clients are happy and I’m leveraging that twenty years of experience.
Finally, a hint. Never let people know how quickly you can get something done. As a writer, I learned early on that most people seriously struggle with writing something like a sales letter. I can literally write something like that in a few minutes, and then charge market value, which can be hundreds to thousands depending on the market (a good sales letter can make that back quickly).